Minimax D-optimal designs for regression models with heteroscedastic errors
| dc.contributor.author | Yzenbrandt, Kai | |
| dc.contributor.supervisor | Zhou, Julie | |
| dc.date.accessioned | 2021-04-20T21:50:47Z | |
| dc.date.available | 2021-04-20T21:50:47Z | |
| dc.date.copyright | 2021 | en_US |
| dc.date.issued | 2021-04-20 | |
| dc.degree.department | Department of Mathematics and Statistics | en_US |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | Minimax D-optimal designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, the minimax D-optimal design problem has an objective function as a difference of two convex functions. An effective algorithm is developed to compute minimax D-optimal designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax D-optimal designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax D-optimal designs. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/12863 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | robust regression design | en_US |
| dc.subject | minimax design | en_US |
| dc.subject | D-optimal design | en_US |
| dc.subject | non-convex optimization | en_US |
| dc.subject | generalized least squares estimator | en_US |
| dc.title | Minimax D-optimal designs for regression models with heteroscedastic errors | en_US |
| dc.type | Thesis | en_US |